Question

Polygon ABCD is translated to create polygon A′B′C′D′. Point A is located at (1, 5), and point A′ is located at (-2, 1). What is the distance from B to B′ ?

Answer 1

The distance from B to B′ is 5 units.

Explanation:

Given data

A = (-2, 1)

A' = (1, 5)

Find the distance between B and B'

We can use the two known points for A to determine the distance between A and A' and the distance formula is

$\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$            = $\sqrt{1-(-2)^2+(5-1)^2}$

                                                     = $\sqrt{25}$

                                                     = 5 units.

Since it is a translation , we know that all points will move the same amount.  So, When A is moved 5 units, B also moves 5 units.

To Learn More...

1.What is polygon ?

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Answer 2

The distance from B to B′ is 5 units.

Explanation:

The distance between two points is given by the formula:

D = √((x₂ - x₁)² + (y₂ - y₁)²)

From given,

(1, 5) = (x₁, y₁)

(-2, 1) = (x₂, y₂)

On substituting the values, we get,

D = √((-2 - 1)² + (1 - 5)²)

D = √((-3)² + (-4)²)

D = √(9 + 16)

D = √(25)

∴ D = 5 units

Since, there is no units such as cm or m is given, the word 'units' is used.